boxcox {MASS} | R Documentation

## Box-Cox Transformations for Linear Models

### Description

Computes and optionally plots profile log-likelihoods for the parameter of the Box-Cox simple power transformation `y^lambda`.

### Usage

    boxcox(object, ...)

    ## Default S3 method:
    boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
           interp, eps = 1/50, xlab = "lambda", ylab = "log-Likelihood", ...)

    ## S3 method for class 'formula':
    boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
           interp, eps = 1/50, xlab = "lambda", ylab = "log-Likelihood", ...)

    ## S3 method for class 'lm':
    boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
           interp, eps = 1/50, xlab = "lambda", ylab = "log-Likelihood", ...)

### Arguments

`object` | a formula or fitted model object. Currently only `lm` and `aov` objects are handled.
`lambda` | vector of values of `lambda` – default (-2, 2) in steps of 0.1
`plotit` | logical which controls whether the result should be plotted.
`interp` | logical which controls whether spline interpolation is used. Default to `true` if plotting with `lambda` of length less than 100.
`eps` | Tolerance for `lambda = 0`; defaults to 0.02
`xlab` | defaults to `"lambda"`
`ylab` | defaults to `"log-Likelihood"`
`...` | additional parameters to be used in the model fitting.

### Value

A list of the `lambda` vector and the computed profile log-likelihood vector, invisibly if the result is plotted.

### Side Effects

If `plotit = TRUE` plots loglik vs `lambda` and indicates a 95% confidence interval about the maximum observed value of `lambda`. If `interp = TRUE`, spline interpolation is used to give a smoother plot.

### References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

### Examples

    data(trees)
    boxcox(Volume ~ log(Height) + log(Girth), data = trees,
           lambda = seq(-0.25, 0.25, length = 10))

    boxcox(Days+1 ~ Eth*Sex*Age*Lrn, data = quine,
           lambda = seq(-0.05, 0.45, len = 20))

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